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Draft version December 24, 2015
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CHARACTERIZING DUST ATTENUATION IN LOCAL STAR FORMING GALAXIES: UV AND OPTICAL
REDDENING
A. J. Battisti1 , D. Calzetti1 R.-R. Chary2
Draft version December 24, 2015
ABSTRACT
The dust attenuation for a sample of ∼10000 local (z . 0.1) star forming galaxies is constrained as
a function of their physical properties. We utilize aperture-matched multi-wavelength data available
from the Galaxy Evolution Explorer (GALEX ) and the Sloan Digital Sky Survey (SDSS) to ensure
that regions of comparable size in each galaxy are being analyzed. We follow the method of Calzetti
et al. (1994) and characterize the dust attenuation through the UV power-law index, β, and the
dust optical depth, which is quantified using the difference in Balmer emission line optical depth,
τBl = τHβ − τHα . The observed linear relationship between β and τBl is similar to the local starburst
relation, but the large scatter (σint = 0.44) suggests there is significant variation in the local Universe.
We derive a selective attenuation curve over the range 1250Å < λ < 8320Å and find that a single
attenuation curve is effective for characterizing the majority of galaxies in our sample. This curve
has a slightly lower selective attenuation in the UV compared to previously determined curves. We
do not see evidence to suggest that a 2175 Å feature is significant in the average attenuation curve.
Significant positive correlations are seen between the amount of UV and optical reddening and galaxy
metallicity, mass, star formation rate (SFR), and SFR surface density. This provides a potential tool
for gauging attenuation where the stellar population is unresolved, such as at high-z.
1. INTRODUCTION
The presence of dust in a galaxy causes its spectral energy distribution (SED) to experience reddening, a consequence of the highest attenuation occurring in the ultraviolet (UV) and decreasing towards longer wavelengths
out to the infrared (IR) (see review by Draine et al. 2003).
The nature of this reddening is dependent on both the
dust properties and its geometry within the galaxy (see
review by Calzetti 2001). Taken together, these effects
limit the interpretation of galaxy SEDs to determine fundamental quantities such as the stellar population age,
stellar mass, and star formation rate (SFR). In the Milky
Way (MW; Cardelli et al. 1989; Fitzpatrick 1999) and
Magellanic Clouds (Gordon et al. 2003), where dust extinction3 can be directly measured using individual stars,
these effects have been well studied and are routinely corrected using extinction curves. The size distribution and
composition of dust grains in these galaxies is directly related to the observed extinction (Weingartner & Draine
2001).
When observing galaxies beyond the MW, the Magellanic Clouds, and other very nearby galaxies (e.g., M31,
Bianchi et al. 1996; Clayton et al. 2015), it is usually
no longer feasible to utilize point sources to derive extinction curves. Exceptions include using quasars (e.g.,
Gallerani et al. 2010) or gamma ray burst (e.g., Perley et
al. 2011). Instead, we must rely on using unresolved stellar populations, which have more complicated SEDs as a
[email protected]
1 Department of Astronomy, University of Massachusetts,
Amherst, MA 01003, USA
2 MS314-6, U.S. Planck Data Center, California Institute of
Technology, 1200 East California Boulevard, Pasadena, CA 91125,
USA
3 We define extinction to be the combination of absorption and
scattering of light out of the line of sight by dust (no dependence
on geometry).
result of being composed of many stars of varying spectral types and will depend on the star formation history
and the initial mass function (IMF). In addition, using
collections of stars, as opposed to single stars, introduces
a wide range of possible geometries for the light sources
with respect to the dust. The nature of this geometry
determines the importance of light scattering into the
line of sight (Calzetti 2001), and is the reason that it
is important to distinguish between extinction and attenuation4 . This additional component has the effect of
flattening or “graying” the overall effective extinction,
due to bluer light experiencing more efficient scattering.
These added complications hinder a general prescription
for correcting for dust attenuation in external galaxies.
One exception to the aforementioned problem has been
for starburst galaxies, for which a tight positive correlation exists between the slope of the UV flux density, β,
and the color excess of the nebular gas, E(B − V )gas ,
which are both related to the wavelength-dependent attenuation (Calzetti et al. 1994). The color excess can
be inferred using the differential optical depth of the
dust from the Balmer decrement, τBl , which we will
term “Balmer optical depth” for sake of brevity. Tight
positive correlations also exist between β and the ratio
of IR to UV luminosity, termed the “infrared excess”
(IRX = LIR /LUV ), which is a proxy for the total dust
attenuation (Meurer et al. 1999). The simple interpretation of the correlation between β and IRX is that dust
attenuation increases with higher dust-to-gas ratios. Unfortunately, the IRX − β correlation has been shown to
break down as one moves from starburst galaxies to more
“normal” star forming galaxies (SFGs) (Kong et al. 2004;
Buat et al. 2005; Hao et al. 2011). This breakdown has
4 We define attenuation to be a combination of extinction and
scattering of light into the line of sight by dust (strong dependence
on geometry).
2
Battisti et al.
been attributed to effects of evolved stellar populations,
different star formation histories, and variations in the
dust/star geometry (e.g., Boquien et al. 2009; Grasha et
al. 2013), all of which can impact the IRX and/or β
values and introduce large scatter.
The influence of dust appears to increase at intermediate redshifts (z ∼ 1 − 3), as the SED of galaxies are
more heavily attenuated by dust than in the local Universe, corresponding to a larger fraction of the star formation within these galaxies being enshrouded by dust
(Le Floch et al. 2005; Magnelli et al. 2009; Elbaz et al.
2011; Murphy et al. 2011; Reddy et al. 2012). These effects can result in imprecise values of SFRs, stellar mass,
extinction corrections, and photometric redshifts of individual galaxies. Uncertainties in the latter two quantities
are among the biggest factors limiting current precision
dark energy studies, affecting both weak-lensing and supernovae measurements. Therefore, it is imperative to
accurately characterize the dust attenuation in galaxies
in order to reduce the uncertainties in the interpretation
of data in future missions that seek to measure cosmological quantities with unprecedented precision. In addition, these quantities are crucial for studies of galaxy
formation and evolution. Understanding the dust attenuation in local SFGs as a function of their properties (e.g.,
metallicity, stellar mass, SFR) creates a baseline with
which to determine appropriate corrections for higher
redshift galaxies. This will allow for accurate determination of galaxy properties when limited measurements
are available, as is typically the case for higher redshift
systems.
For their sample of 39 local starburst galaxies, Calzetti
et al. (1994) find a linear correlation between β and τBl .
This result implies that the dust behaves as a foreground
distribution to the ionized gas, because in this scenario
the reddening of the stellar continuum linearly correlates
with the reddening of nebular regions. They derive the
selective attenuation for this sample by comparing the
average SEDs of galaxies binned according to τBl . Virtually all studies of SFGs, both local and distant, make
use of the attenuation curve derived from this sample
(Calzetti et al. 2000) to correct for effects of dust and
determine properties of those galaxies. The appeal of
this method stems from its simple approach; determining
rest-frame UV colors (β), which correspond to observerframe optical colors for high-z galaxies, allows for the
dust-free luminosity to be recovered. However, since the
Calzetti et al. (2000) attenuation curve was calibrated
with a relatively small number of local starburst galaxies, it is not clear how accurate such generalizations are
to more typical SFGs with lower specific star formation
rates (sSFRs; SFR/M∗ ). More importantly, the extent
to which the relation holds true as a function of redshift
has not been conclusively determined. Recent results by
Reddy et al. (2015) suggest that the relationship between
β and τBl is shallower for galaxies at z ∼ 2 and is dependent on the sSFR. They also find that the attenuation
curve for these galaxies is lower by about 20% in the
UV. A similar study of a large number of local SFGs will
provide a strong foundation with which to compare and
address why such differences exist.
Other studies have examined the nature of attenuation for large samples of local galaxies (e.g., Johnson et
al. 2007b; Wild et al. 2011) in order to address the degree
to which it can vary. However, these studies have used
different techniques than those described in Calzetti et
al. (1994, 2000), which can introduce different biases and
make direct comparison unclear. More specifically, Johnson et al. (2007b) use average SEDs of galaxies separated
according to IRX and Wild et al. (2011) utilize a galaxy
pair-matching technique (matched in gas-phase metallicity, sSFR, axial ratio, and redshift) to compare the SEDs
of more dusty and less dusty galaxies as determined by
τBl . Despite the different methods for constructing attenuation curves among these studies, a common picture
has developed in which the dust content of galaxies appear to have two components (e.g., Calzetti et al. 1994;
Charlot & Fall 2000; Wild et al. 2011); one associated
with short-lived dense clouds where massive stars form
HII regions and another associated with the diffuse interstellar medium.
For this study, we follow the methodology used in
Calzetti et al. (1994) to determine the behavior of dust
attenuation in a large sample of SFGs with a wide range
of properties in order to test the extent to which the dust
attenuation and geometry found in that work might hold
for a more diverse sample of galaxies. Understanding the
geometry of the dust in these systems gives important information on where dust is located in galaxies. The large
sample size will also allow us to examine sources of scatter in the attenuation properties of individual galaxies.
Furthermore, our results will allow for more detailed future analysis into the nature of the IRX − β relationship
breakdown for normal SFGs at z ∼ 0.
Throughout this work we adopt a Λ-CDM concordance
cosmological model, H0 = 70 km/s/Mpc, ΩM = 0.3,
Ωvac = 0.7. We also assume a Kroupa IMF (Kroupa
2001) when making comparisons with stellar population models. To avoid confusion, we make explicit distinction between the color excess of the stellar continuum E(B − V )star , which traces the reddening of the
bulk of the galaxy stellar population, and the color
excess seen in the nebular gas emission E(B − V )gas ,
which traces the reddening of the ionized gas around
massive stars located within HII regions. In principle these two parameters need not be related because
E(B − V )star and E(B − V )gas are a result of attenuation and extinction, respectively (i.e., they use different obscuration curves; see § 3.1), but they have
been found to be correlated in starburst galaxies, with
hE(B − V )star i = (0.44 ± 0.03)hE(B − V )gas i (Calzetti et
al. 2000), and in star forming regions within local galaxies, with hE(B − V )star i = (0.470 ± 0.006)hE(B − V )gas i
(Kreckel et al. 2013).
2. DATA AND MEASUREMENTS
2.1. Sample Selection
Our sample is constructed using the Galaxy Evolution
Explorer (GALEX ; Martin et al. 2005; Morrissey et al.
2007) catalogs of Bianchi et al. (2014). These catalogs
represent unique sources in the GALEX data release 6/7
(GR6/7) and are separated for the All-sky Imaging Survey (AIS; depth mAB ∼ 20.5 mag in FUV/NUV), containing ∼71 million sources, and the Medium Imaging
Survey (MIS; depth mAB ∼ 22.7 mag), containing ∼16.6
million sources (Bianchi et al. 2014). We only make use
Characterizing Dust Attenuation in Local Star Forming Galaxies
of sources that can be cross-matched to the Sloan Digital Sky Survey (SDSS) data release 7 (DR7; Abazajian et
al. 2009) sources and have available SDSS spectroscopy,
as the latter is required to determine the Balmer decrement. These cross-matched cases are determined using the Mikulski Archive for Space Telescopes (MAST)
CasJobs website5 , with the requirement that the separation between objects be within 3′′ to be a match. Since
our analysis requires detection in both the GALEX FUV
(1344−1786 Å) and NUV (1771−2831 Å) bands, we have
chosen to only consider galaxies within the MIS catalog because spectroscopic SDSS galaxies detected within
both bands in the shallower AIS are found to be highly
biased towards very blue galaxies (see § 4.2 for details).
Within the MIS catalog, this restricts the parent sample
to 63691 galaxies.
For the purpose of this study, we further constrain
the sample to only star forming galaxies (SFGs) and exclude cases in which a significant fraction of the flux density is produced from an active galactic nucleus (AGN).
The galaxy type is determined using the traditional optical emission line diagnostics [NII]λ6583/Hα, a proxy for
gas phase metallicity, and [OIII]λ5007/Hβ, a measure
of the hardness of the radiation field (i.e., the BaldwinPhillips-Terlevich (BPT) diagram, Baldwin et al. 1981;
Veilleux & Osterbrock 1987; Kewley et al. 2001; Kauffmann et al. 2003c). The optical spectroscopic measurements for these galaxies are from the Max Planck Institute for Astrophysics and Johns Hopkins University
(MPA/JHU) group6 , which is based on the method presented in Tremonti et al. (2004). To summarize, line
fluxes are corrected for stellar absorption by fitting a
non-negative combination of stellar population synthesis
models from Bruzual & Charlot (2003) for the SDSS DR4
and updated in DR7 using a newer version of these models (unpublished). As recommended by the MPA/JHU
group starting with DR4, we increase the uncertainties
associated with each emission line. We adopt the values listed in Juneau et al. (2014), which are updated for
the DR7 dataset. It has been found by Groves et al.
(2012) that the equivalent width of the Hβ emission line
of galaxies in the MPA/JHU catalog appear to be underestimated by ∼0.35 Å due to their method of correcting
Balmer absorption. However, this correction value was
derived assuming these galaxies follow the Calzetti et al.
(2000) attenuation curve and because we are seeking to
determine if there are significant departures from that
relation, we choose not to adopt it. We have examined
the effect of including this correction and found that it
causes a systematic decrease in the estimated Balmer optical depth of ∆τBl ∼ −0.1. As was seen in Groves et al.
(2012), we find this shift to be uniform across the entire
range of Balmer emission line strengths (i.e., τBl values).
For this reason, we expect that this will not influence the
attenuation curve derived later because only the difference in Balmer optical depth is used and not the absolute
value.
We require that all emission lines have a signal-tonoise ratio (S/N ) greater than 5 for classification, with
the additional constraint that the FUV and NUV mea5
6
http://galex.stsci.edu/casjobs/
http://www.mpa-garching.mpg.de/SDSS/DR7/
3
surements have S/N > 5 and that the redshift of the
galaxy be z ≤ 0.105. The redshift restriction is required to ensure that the FUV passband (λFUV =1516 Å,
FWHM=269 Å) lies above the numerous stellar absorption features that occur below 1250 Å. Using this selection criteria gives a final sample of 9813 SFGs.
All photometry and spectroscopy has been corrected
for foreground Milky Way extinction using the GALEX
provided E(B − V )MW with the extinction curve of Fitzpatrick (1999). For the GALEX bands, we adopt the values of kFUV = 8.067 and kNUV = 8.05, which represent
the average value of the MW extinction curve convolved
with each filter on SEDs with UV slopes −2.5 < β < 0.5,
the typical range for our SFG sample.
All measurements of galaxy properties utilized in this
work are those provided by the MPA/JHU group and
correspond only to the 3′′ SDSS fiber, which is typically
centered on the nuclear region and represents only a fraction of the total galaxy. The stellar masses are based
on fits to the photometric data following the methodology of Kauffmann et al. (2003a) and Salim et al. (2007).
The SFRs are based on the method presented in Brinchmann et al. (2004). The gas phase metallicities are estimated using Charlot & Longhetti (2001) models as outlined in Tremonti et al. (2004). The fiber regions of
the 9813 SFGs in this sample span the following range
in properties: 5.99 < log[M∗ (M⊙ )] < 10.67, −3.66 <
log[SF R(M⊙ yr−1 )] < 1.60, and 7.67 < 12 + log(O/H) <
9.37. For comparison with Calzetti et al. (1994), our
sample consists of galaxies with lower sSFRs (average
Hα emission equivalent width, hEW(Hα)i ∼ −40 Å;
a proxy for sSFR) relative to their starburst sample
(hEW(Hα)i ∼ −110 Å; McQuade et al. 1995; StorchiBergmann et al. 1995).
2.2. UV-Optical Aperture Matching
In order to test the existence of any relation between
the UV flux density measured by GALEX and the optical
flux density measured by SDSS it is crucial that the apertures be closely matched in order to ensure the they arise
from regions of the galaxy that are comparable in size.
This is also essential in order to utilize the SEDs of these
galaxies to derive the underlying attenuation curve. The
limiting factor in this respect is the 3′′ diameter of the
SDSS spectroscopic fiber. This aperture is smaller than
the point-spread function (PSF) of GALEX at both FUV
(FWHM = 4.2′′ ) and NUV (FWHM = 4.9′′ ). Using an
aperture which is smaller than GALEX PSF would add
positional uncertainty that could introduce UV emission
unassociated with the fiber location. However, using an
aperture much larger than the PSF would require large
aperture corrections for our fiber measurements, which
would also introduce uncertainty. In addition, the large
PSF of GALEX can lead to nearby objects contributing
to the observed flux density within a given area and using a large aperture would increase the likelihood of this
happening. As a compromise between these issues we
choose to adopt a 4.5′′ diameter aperture for our analysis. The UV photometry and associated uncertainties
at this aperture were retrieved directly from the MAST
database using CasJobs. We note that by adopting a
7
k(λ) ≡ Aλ /E(B − V ) is the total-to-selective extinction.
4
Battisti et al.
fixed aperture, the physical sizes being probed will vary
from sub-kpc at the lowest redshifts up to several kpc at
the higher redshifts (0.002 ≤ z ≤ 0.105). We address the
impact of this effect on our results in § 6.2 & 6.3 when
we separate the sample according to redshift.
Given that the chosen aperture is roughly the size of
the PSF for the GALEX bands, determining the appropriate aperture corrections for the UV is non-trivial as
a significant amount of light from outside of the aperture region can be spread within it. To distinguish these
effects we utilize the light profile models of SDSS galaxies from the NYU Value-Added Galaxy Catalog8 (NYUVAGC; Blanton et al. 2005). These profiles are onecomponent Sérsic fits of each individual band of SDSS,
i
h
(1)
I(r) = A exp −(r/r0 )1/n ,
where A is an amplitude in nanomaggies/arcsec2, r0 is
an effective radius in arcsec, and n is the Sérsic index.
A nanomaggie is a flux density unit defined such that
1 nanomaggie has a magnitude of 22.5 in any band,
mAB = 22.5 − 2.5 log[f (nMgy)], which for SDSS as a
near AB magnitude system is 3.631 µJy. If we assume
that the UV colors follow the u-band light profile, which
is the shortest wavelength SDSS band, then it is possible
to determine appropriate aperture corrections for each
individual galaxy. This is done by measuring the amount
of light within 4.5′′ in the modeled u-band profile, Fref ,
and comparing this to the same measurement after the
light profile has been convolved with the GALEX PSFs,
FUV . These PSFs are obtained from the GALEX data
analysis website9 . The aperture correction is taken as the
ratio of these values, Fref /FUV . The distribution of aperture corrections for the entire parent sample of galaxies
is shown in Figure 1. Roughly one-third of the sources
in our sample are well approximated as point sources in
GALEX (corresponding to being near the peak in the
distribution). The aperture correction in flux density for
a point-source is a factor of 2.29 and 2.86 for FUV and
NUV, respectively.
It can be seen in Figure 1 that there are some sources
with aperture corrections that are larger than what is
expected for a point source (vertical dashed lines). To
determine the cause of this interesting behavior we examined the relationship between the aperture corrections
with the effective radius of the galaxy and its Sérsic index in the u-band. We choose to use the 90% light radius
from the NYU-VAGC light profile, r90,u , instead of the
variable r0 in the Sérsic fit, as it is a better representation
of the size of the galaxy. We find that the behavior of
the aperture correction is directly related to r90,u and the
Sérsic index, which we illustrate in Figure 2 and discuss
below.
We find that sources with radii of r90,u . 1′′ or with
r90,u & 1′′ and large Sérsic indices (i.e., steep light profile) are well described by a point-source correction (see
panel (a) in Figure 2). For the regime of galaxies with
1′′ . r90,u . 3′′ and small Sérsic indices (i.e., shallow
light profile), there is little galaxy flux density outside
of the 4.5′′ aperture to spread inside of it, due to the
smearing effect of the PSF, but the light within it is be8
9
http://sdss.physics.nyu.edu/vagc/
http://www.galex.caltech.edu/researcher/techdoc-ch5.html
Figure 1. Histogram of the flux in 4.5′′ apertures based on the
SDSS u-band Sérsic light profile, Fref , relative to the flux within the
same aperture after convolving u-band light profile by the GALEX
PSFs, FUV , for the 9813 SFGs in our sample. This ratio corresponds to the aperture correction, Fref /FUV , under the assumption
that the UV light follows a similar behavior to that of the u-band.
Roughly half of the sources are well approximated as point-sources,
which corresponds to the peaks in the distributions (vertical dashed
lines).
ing spread out more than would be the case for a pointsource. Together these effects result in a larger aperture
correction being necessary than would be the case for
a point-source (see panel (b) in Figure 2). For galaxies
with r90,u & 3′′ and small Sérsic indices, there is significant light outside of the 4.5′′ aperture that can be spread
into it and we find an aperture correction that is smaller
than that for a point-source (see panel (c) in Figure 2).
Since we have chosen to adopt a 4.5′′ aperture for our
galaxies, we also need to apply an aperture correction to
the SDSS spectroscopy (3′′ ). Following a similar methodology to before, we determine the correction for the observed photometry using the light profile models from the
NYU-VAGC. The correction is taken to be the ratio of
light within 4.5′′ and 3.0′′ in the modeled band profile.
We then perform a chi-squared minimization to match
the optical spectrum to the 4.5′′ photometry.
All nebular line diagnostics used in this study are ratios
of emission lines ([NII]/Hα, [OIII]/Hβ, and Hα/Hβ), and
the effects of the aperture corrections are very small. The
reason for this is because the relative difference in the correction terms across the SDSS bands is small (∼ 6%, 1σ
dispersion of 11%). As a check, we estimated a correction for each the optical emission lines by taking a linear
interpolation between the corrections of the two closest
bands. The largest aperture effects for the line ratios will
occur for lines which are separated the furthest in wavelength; which in this study is the ratio of the Hα to Hβ.
We find that the distribution of the ratio of the aperture corrections for Hα to Hβ has a mean of 0.98, with a
1σ dispersion of 0.03. This implies these corrections will
only change the ratio measurements at the level of a few
percent and will be even smaller for the other line ratios
(≪ 1%). As these are minor changes we have chosen not
to apply any aperture corrections to the emission lines.
As a check on the accuracy of the aperture matching, we compare the corrected UV flux densities to the
Characterizing Dust Attenuation in Local Star Forming Galaxies
5
corrected optical spectra and inspected if the shape of
the UV (inferred from βGLX ) agrees with the shortest wavelength data available in the optical spectrum
(λ ∼ 3600 Å, for z ∼ 0.05). In other words, we examine
whether the region between 2600 − 3600 Å, corresponding to the gap in our data, that would be extrapolated
from the UV slope and the optical data shortward of the
4000 Å break feature are in agreement. If our aperture
corrections are inaccurate, then we expect to see systematic offsets between the flux densities in the UV and
optical. As will be shown with our average templates in
§ 4.3, we find that on average the UV data agrees well
with the optical data, with no significant offsets between
them.
3. METHODOLOGY FOR CHARACTERIZING
ATTENUATION
3.1. Balmer Optical Depth
The dust attenuation in a galaxy can be measured from
the optical depth, τ (λ). For the simple case of a uniform
layer of dust between a source of intensity, Iλ0 , and the
observer, the optical depth is defined as
Iλ = Iλ0 e−τ (λ) ,
Figure 2. Demonstration of how different galaxy light profiles
affect the aperture correction (Fref /FUV ). The red circle represents the 4.5′′ aperture. The surface brightness profiles have been
normalized such that the aperture flux density (shown in red) in
the u-band value is 1 µJy. (a) Galaxies with radii of r90,u . 1′′
or r90,u & 1′′ and large Sérsic indices (i.e., steep light profile) are
well described as point-sources. (b) Galaxies with 1′′ . r90,u . 3′′
and small Sérsic indices (i.e., shallow light profile) have the light
within 4.5′′ being spread out more than would be the case for a
point-source and this leads to smaller FFUV relative to case (a).
(c) Galaxies with r90,u & 3′′ and small Sérsic indices have significant light outside of the 4.5′′ aperture that can be spread into it
and we find larger FFUV relative to case (a). The NUV aperture
corrections behave in a similar manner.
(2)
where Iλ is the observed intensity and all quantities are
dependent on the wavelength. In the case of a point
source such as a star with a well-characterized SED, the
optical depth can easily be determined by comparing the
observed and intrinsic SEDs. However, in the case of
entire galaxies for which the underlying SED is strongly
affected by many factors, including the underlying stellar population, star formation history, and IMF, this becomes much more difficult. To mitigate these problems
the flux ratio of Hα and Hβ is often utilized, as the intrinsic flux ratio is set by quantum mechanics and is only
affected by the electron temperature, Te , and density, ne ,
at the ∼ 5 − 10% level (Osterbrock & Ferland 2006).
This ratio is also relatively insensitive to the underlying
stellar population and IMF (Calzetti 2001). Therefore,
large variations from the intrinsic ratio can be directly
attributed to the reddening of dust.
For our work we will use the Balmer decrement,
F (Hα)/F (Hβ), as a tracer of dust attenuation, with the
assumption that this dust acts as a foreground screen
for these lines. Since the ionized gas from which these
lines arise is primarily located in HII regions, which have
small angular extent relative to the rest of the galaxy
(and presumably the dust), and are usually distributed
within a short height of the galaxy’s midplane, this is a
reasonable assumption. Following from equation (2) and
Calzetti et al. (1994), we define the Balmer optical depth
as
F (Hα)/F (Hβ)
,
(3)
τBl = τHβ − τHα = ln
2.86
where F (Hα) and F (Hβ) are the flux of the nebular emission lines located at 6562.8 Åand 4861.4 Å, respectively,
and the value of 2.86 comes from the theoretical value expected for the unreddened ratio Hα/Hβ undergoing Case
B recombination with Te = 104 K and ne = 100 cm−3
(Osterbrock 1989; Osterbrock & Ferland 2006). The superscript l is used to emphasize that this quantity is coming from emission lines and should be distinguished from
6
Battisti et al.
optical depths associated with the stellar continuum. If
one assumes knowledge of the total-to-selective extinction, k(λ) ≡ Aλ /E(B − V ), then τBl can be directly related to the color excess of the nebular gas, E(B − V )gas ,
through
1.086τBl
A(Hβ) − A(Hα)
=
,
k(Hβ) − k(Hα)
k(Hβ) − k(Hα)
(4)
where A(λ) is the total extinction at a given wavelength.
If the extinction in other galaxies at these wavelengths
were to be identical to the MW, which is unlikely to
always be the case, then we can use k(Hα) − k(Hβ) =
1.257 (Fitzpatrick 1999).
Since the hydrogen recombination lines are primarily
produced within the HII regions of massive O and B
stars, this implies that they are only sensitive to the attenuation of ionized gas around these massive stars. In
general these same stars will also contribute greatly to
the UV and optical light of the total stellar population,
leading one to expect the reddening of the ionized gas to
be related to the reddening seen in the stellar population
(traced by β or E(B − V )star ). However, the distribution
of these massive stars and the rest of the stellar population relative the distribution of dust, in addition to the
age distribution of the stellar population (i.e., the relative contribution of older stars to the UV-optical flux
density), will strongly influence how these quantities are
related. For both starburst galaxies (Calzetti et al. 2000)
and star forming regions within local galaxies (Kreckel
et al. 2013) it appears that the stellar continuum suffers roughly one-half of the reddening of the ionized gas.
This result suggests a scenario in which massive stars
are more deeply embedded in molecular clouds than the
long-lived stars (e.g., see descriptions in Charlot & Fall
2000, Calzetti 2001, or Wild et al. 2011). Another concern is that the total amount of dust within a galaxy may
only weakly relate to attenuation, as the regions of lowest optical depth (τBl . 1) are providing the majority of
the flux density (Calzetti et al. 1994). Large amounts of
the dust might exist in the regions of high optical depth
(τBl >> 1), which would provide negligible amounts of
flux density and thus not be represented by our tracers.
Fortunately, the presence of dust attenuation beyond the
level of what can be measured in the optical has not been
shown to be an issue for local starburst galaxies (Meurer
et al. 1999), and therefore we do not expect this to be a
major concern.
E(B − V )gas =
3.2. UV Slope
For actively SFGs, where the UV is dominated by recent star formation (i.e., massive stars) and there is little
contamination from earlier generations of stars, the dust
attenuation can also be measured from the UV flux density spectral slope, β, which is defined as
F (λ) ∝ λβ ,
(5)
where F (λ) is the flux density in the range 1250 ≤
λ ≤ 2600 Å. For reference, β values cover the range
between −2.70 and −2.20 for constant star formation
(i.e., they have a fairly small intrinsic variation; Calzetti
2001). This makes this parameter ideal for measuring
the wavelength-dependence of attenuation in the UV. In
Appendix A, we examine the use of the optical slope as
dust tracer when UV data is unavailable.
For this study, we use the UV power-law index βGLX
measured from observed GALEX FUV and NUV photometry,
βGLX =
log[Fλ (FUV)/Fλ (NUV)]
,
log[λFUV /λNUV ]
(6)
where the flux density is in erg s−1 cm−2 Å−1 , λFUV =
1516Å/(1 + z), and λNUV = 2267Å/(1 + z). If one assumes a power-law fit to the region described above, there
is no need to perform k-corrections on the flux density.
We examine the possibility of a 2175 Å absorption feature biasing this UV slope measurement in § 5.2. As is
shown in Calzetti et al. (1994), the quantities τBl and
β can be used to derive a dust attenuation curve independent of any prior knowledge of its shape. Such an
analysis will be performed in § 4.3.
4. DUST ATTENUATION IN STAR FORMING GALAXIES
4.1. Relating Attenuation of UV Continuum to the
Balmer Optical Depth
In order to characterize the dust attenuation in SFGs,
we first examine how the reddening in the UV stellar
continuum (measured through βGLX ) is related to the
optical reddening of the ionized gas (measured through
τBl ). In Figure 3 we show the βGLX and τBl values for our
sample of 9813 SFGs. There does appear to be a significant correlation present, but with a large degree of scatter. Spearman and Kendall nonparametric correlation
tests give ρS = 0.48 and τK = 0.33, respectively, which
indicate that this correlation is not particularly strong.
Given the large sample size we are dealing with, it is
not possible to report the significance of these correlation coefficients because the probability of no correlation
existing is found to be very close to zero.
Looking at Figure 3, it can be seen that there are a
number of cases for which τBl < 0. This corresponds to
cases where the observed flux ratio of the Balmer lines
is below the assumed intrinsic value of 2.86. This can
result from the uncertainties in the measured values of
these lines (see representative error bar) or from variations in the intrinsic line ratio (e.g., for Te > 104 K
and/or ne > 100 cm−3 the intrinsic ratio decreases; Osterbrock & Ferland 2006). Another interesting feature is
the lack of data points at τBl & 0.7, which corresponds to
galaxies experiencing the largest attenuation. It is worth
determining if this is being driven by the selection criteria imposed for our sample, which requires the UV flux
density and emission line fluxes to have S/N > 5, and if
it could result in any biases. We postpone the analysis
of a UV selection bias until § 4.2, where we will compare
sources from GALEX surveys of different depths. To test
for an emission line selection bias, we examine the effect
that requiring a lower S/N threshold for the weakest line
in this study ([OIII]λ5007) has on the sample being selected. Imposing a threshold of S/N > 3 for [OIII]λ5007,
while still requiring S/N > 5 for the other lines, increases
the sample size by 2160 galaxies. Imposing lower thresholds on the other lines does not increase the sample size
significantly. We do find that the weaker [OIII] systems
are slightly more attenuated on average than the original
7
Characterizing Dust Attenuation in Local Star Forming Galaxies
Table 1
l Bins
Values of τB
Bin
l < 0.10
−0.26 ≤ τB
l < 0.20
0.10 ≤ τB
l < 0.30
0.20 ≤ τB
l < 0.40
0.30 ≤ τB
l < 0.50
0.40 ≤ τB
l < 1.01
0.50 ≤ τB
N
1303
2244
2533
1913
1101
719
l i
hτB
0.04 ± 0.09
0.15 ± 0.07
0.25 ± 0.07
0.35 ± 0.06
0.44 ± 0.06
0.59 ± 0.09
hβGLX i
−1.37 ± 0.54
−1.22 ± 0.54
−1.00 ± 0.54
−0.83 ± 0.57
−0.62 ± 0.61
−0.37 ± 0.72
hβi
−1.52 ± 0.55
−1.37 ± 0.55
−1.15 ± 0.54
−0.98 ± 0.58
−0.77 ± 0.62
−0.52 ± 0.74
l spanned, (2) number of
Notes. Columns list the (1) range in τB
objects, (3) weighted-mean Balmer optical depth (see § 3.1), (4)
weighted-mean UV slope using the GALEX passbands (see § 3.2),
(5) weighted-mean UV slope after correcting for stellar absorption
features in the GALEX passbands (see § 5.1). The uncertainties
shown correspond to the measurement uncertainty and the sample
dispersion added in quadrature.
Figure 3. The UV power-law index, βGLX , as a function of the
l , for our sample of SFGs. A representative
Balmer optical depth, τB
error bar of the median measurement uncertainties for our sample
is shown in the top left. A linear least-squares fit with error in
both variables while also including a term to account for intrinsic
l > 0.7 is
scatter in the data is shown (orange line). Our fit at τB
shown with a dashed line to denote that there are limited data in
this range. For comparison, the data are separated into six bins of
l (red squares; see Table 1).
τB
sample (i.e., larger βGLX & τBl ), but the vast majority
are still τBl < 0.7. Including these galaxies has no effect
on the relationship between βGLX and τBl . Therefore, we
believe that we are not preferentially excluding objects
located at τBl & 0.7. The lack of objects at these values
may result from galaxies at this level of attenuation being
relatively rare in the local Universe, which is consistent
with the results of Kauffmann et al. (2003a).
Similar to the findings of Calzetti et al. (1994), the
observed relationship between βGLX and τBl is linear,
which indicates that the dust behaves as a foregroundlike screen to ionized gas regions. We fit a linear relationship to the data in Figure 3 using the MPFITEXY
routine (Williams et al. 2010), which utilizes the MPFIT
package (Markwardt 2009). This routine performs a linear least-squares fit with error in both variables while also
including a term to account for intrinsic scatter in the
data. A scatter within the data is expected for the y-axis
given that βGLX is likely to be dependent on variations
in the age of the stellar population, the star formation
history, and/or the metallicity of each galaxy (Calzetti
et al. 1994). A fit to the βGLX and τBl values for all of
the data gives
βGLX = (1.96 ± 0.03)τBl − (1.46 ± 0.01) ,
(7)
with an intrinsic dispersion of σint = 0.43. We denote
the region of τBl > 0.7 in our fit with a dashed line to
indicate that there are limited data in this range. Interestingly, the width of the scatter in βGLX does not
appear to change with τBl . As a result of this behavior,
we do not expect the scatter to be strongly driven by
possible variations in the dust geometry. This is because
the scatter around the value of βGLX should decrease
for “low-dust” systems (τBl ∼ 0), regardless of geometry,
and approach the intrinsic value of βGLX for each galaxy
(e.g., see Calzetti et al. 1994, 2000). We will examine
this scatter in more detail in § 6.2.
We also examine the data after binning it into 6 bins
of τBl , which is useful for comparison in our derivation of
the attenuation curves in § 4.3. The ranges of the bins
along with their weighted-mean values, which account
for uncertainties in both variables, are shown in Table 1.
The error bar shown for each bin correspond to the measurement uncertainty and the sample dispersion added
in quadrature. It can be seen that these bins are in good
agreement with the previous fit, given the uncertainties.
We postpone a comparison of our βGLX − τBl relation to
those in the literature until § 5.1, as we will make use
of our derived attenuation curve to determine an appropriate way to compare different techniques for measuring
the UV slope.
4.2. Tests on Possible UV Selection Effects
As mentioned in § 2.1, we did not use the GALEX AIS
sample for our analysis as it was realized that sources detected in both FUV and NUV in this survey are biased
towards galaxies with blue UV slopes. We attribute this
bias to the shallowness of the AIS. This effect is identical
to selection biases which occur for high redshift galaxies
(e.g., Dunlop et al. 2012; Bouwens et al. 2012) and is a
result of sources at the detection threshold being preferentially identified if they have bluer colors. In this section
we demonstrate the bias in the AIS sample and also show
that no such bias is evident for the MIS.
Following the same approach outlined for the MIS sample, we select sources in the AIS that have FUV and NUV
data with S/N > 5 and are designated as SFGs using the
BPT diagram. This gives a sample of 3190 galaxies in
the AIS. We plot the values of βGLX vs. τBl for the galaxies detected in these two survey in Figure 4. Looking at
this Figure, it is apparent that galaxies in the AIS are
bluer with relatively small Balmer decrements (indicative of less dust) relative to MIS. This result suggests
that the shallowness of the AIS is such that only galaxies with minimal attenuation can be detected in both UV
bands. It is worth pointing out that Wild et al. (2011)
use GALEX AIS data for their analysis and this may account for differences in the UV region of the attenuation
curve derived later in this study and theirs.
In light of the previous issue, we feel it necessary to
check whether or not similar effects could be biasing the
8
Battisti et al.
l relation for galaxies in the
Figure 4. Comparison of the βGLX -τB
GALEX AIS and MIS surveys (depths of mAB ∼ 20.5 mag and
mAB ∼ 22.7 mag, respectively) that satisfy our selection criteria.
It is apparent that the sample in the shallower AIS survey is biased towards bluer galaxies (lower βGLX ) with relatively little dust
l ) compared to the sample from the deeper MIS survey.
(lower τB
For this reason the AIS sample was excluded from our analysis.
sample of galaxies selected in the MIS. To perform this
test we examine galaxies within the Galaxy Multiwavelength Atlas from Combined Surveys (GMACS) dataset,
which was observed with GALEX as part of its deep
imaging survey (DIS). The regions within the GMACS
sample consist of the Lockman Hole, the Spitzer First
Look Survey (FLS), and the SWIRE ELAIS-N1 and N2
fields. Unlike the MIS and AIS, the exposure times for
different fields in the DIS can have significantly different
exposure time but the typical depth is mAB ∼ 25 mag.
This subsample of the DIS was chosen because the catalog of the cross-matched SDSS spectroscopic sources is
publicly available10 .
Following the same approach outlined for the MIS sample, we select sources in the GMACS sample that have
FUV and NUV data with S/N > 5 and are designated
as SFGs using the BPT diagram. This gives a sample of
476 galaxies. We plot the values of βGLX vs τBl for this
sample of galaxies compared to the MIS sample in Figure 5. A visual comparison suggests that this population
appears to occupy a similar region of parameter space
compared to the MIS sample. We take a LLS fit, with
an added term for scatter, and find the relation,
l relation for galaxies in the
Figure 5. Comparison of the βGLX -τB
GALEX GMACS and MIS surveys (depths of mAB ∼ 25 mag and
mAB ∼ 22.7 mag, respectively) that satisfy our selection criteria.
l parameter
These two samples occupy similar regions of βGLX -τB
space, despite having different depths. Therefore, we suspect that
the MIS sample does not suffer from a UV-selection bias.
in the MIS selected sample is also nearly Gaussian with
µ = 0.25 and a dispersion of σ = 0.15. This would further argue that there is not a significant fraction of the
full population that are missed as a result of the UV flux
requirement.
4.3. Deriving the Dust Attenuation Curve
The main drawback in utilizing entire galaxies for deriving attenuation curves is that their spectra result from
the contributions of many stellar populations of different
ages, and therefore we have no knowledge of the underlying intrinsic spectra with which to directly compare (in
contrast to using individual stars for extinction curves).
However, given the large dataset on hand, we can take a
statistical approach to determine the attenuation curve
if we assume that the effects of different stellar populations, which should only significantly affect βGLX , can
be averaged out within similar values of τBl . This is the
same approach taken in Calzetti et al. (1994) and Reddy
et al. (2015) to derive their attenuation curves.
Before proceeding with the methodology described
above, it is important to determine whether or not there
are any systematic trends between our attenuation parameters and the stellar population age in order to ensure
that the average age of each template for different bins
βGLX,GMACS = (2.08 ± 0.11)τBl − (1.61 ± 0.03) , (8)
in τBl are consistent. One way to test this is by examinwith an intrinsic dispersion of σint = 0.36. This relation
ing the value of the 4000 Å break and the sSFR, both of
is consistent with our original sample given the uncerwhich are sensitive to the age of the stellar population, as
tainties and scatter. This implies that the UV depth of
a function of βGLX and τBl in our galaxy sample. We utithe MIS sample does not significantly bias our sample
lize the measurement of Dn 4000 for the 4000 Å break and
towards galaxies of a particular attenuation.
the galaxy SFR and stellar mass (M∗ ) within the specAs a final check, we also examined the distribution of
troscopic fiber from the MPA/JHU catalog. The coml
τB values for the entire SDSS spectroscopic sample idenparison between these two parameters and βGLX and τBl
tified as a SFG using the BPT diagnostics with emission
is shown in Figure 6. It can be seen that there are slight
line strengths of S/N > 5 and z ≤ 0.105 but without
changes
in the range of βGLX or τBl values spanned at a
requiring any UV detection. This selection gives a saml
given Dn 4000 value, suggesting that larger values of τBl
ple of ∼150000 galaxies with a distribution of τB values
might correspond on average to galaxies with a slightly
which is nearly Gaussian with a mean of µ = 0.26 and
larger Dn 4000 values (older stellar population). No oba dispersion of σ = 0.17. The range of values observed
vious trends appear evident when comparing to sSFR.
10 http://user.astro.columbia.edu/ bjohnson/GMACS/catalogs.html
If the trend with Dn 4000 is indeed significant, then we
~
Characterizing Dust Attenuation in Local Star Forming Galaxies
should see a noticeable difference among the inferred attenuation curves for the different bins of τBl as a result
of using the lower τBl bins for comparison.
As a first attempt for deriving an attenuation curve,
we work under the assumption that the average flux density of the spectra within all bins of τBl create template
spectra which represent galaxies with the same average
stellar population age. The adopted bins are outlined in
Table 1. In order to reduce the large spread in flux density values within each bin, which result from the range
of distances covered by our sample, we normalize the flux
density to the rest-frame value at λ = 5500 Å. Since we
are interested in understanding the attenuation of the
stellar continuum, we make use of the available emission
line subtracted optical spectra from the SDSS database
for each galaxy. Each optical spectrum is smoothed by
50 channels (∼ 40 − 100 Å) to improve the S/N . The
flux density in the UV region of 1250 < λ < 2600 Å
is determined solely based on the two bands covered by
GALEX under the assumption that the entire region follows the βGLX power-law behavior determined from the
FUV and NUV, and we acknowledge this as a limitation
of this study. Such an assumption would not distinguish
possible features within the attenuation curve, such as a
2175 Å bump. Although if a feature is present, it would
impact the values of βGLX and we will discuss this in
more detail in § 5.2. We also note that βGLX is slightly
redder than the actual UV spectrum (see § 5.1), but because we are using the ratio of flux densities for our analysis, the outcome for the attenuation curve is the same
regardless of this effect.
For constructing our templates we choose not adopt
a weighted-mean, as is done in Calzetti et al. (1994),
because we find that the reddest galaxies (largest βGLX )
within each bin tend to be brighter and have lower uncertainties, which biases the average UV slope of the templates to larger values of βGLX for all bins (∆βGLX ∼
0.2). In contrast, adopting a simple average of the flux
densities creates templates which have a UV slope nearly
identical to the value found by taking the weighted-mean
of all βGLX within that bin (∆βGLX ∼ 0.02). For deriving the attenuation curve we are only considering the
optical spectral region for which every galaxy has data.
For z < 0.1, this corresponds to 3793 ≤ λ ≤ 8325 Å.
Given that the βGLX -τBl relation of this sample demonstrates similarity to the results of Calzetti et al. (1994),
it would appear that the dust geometry is similar to that
of starbursting systems (namely a foreground-like geometry). In this scenario, the optical depth is expected
to follow a functional form similar to equation (2) and
we can use the flux density from lower bins of τBl as a
reference spectrum (i.e., representing lower attenuation
cases).
Given a reference spectrum, Fr (λ), we can determine
τn,r (λ) = − ln
Fn (λ)
,
Fr (λ)
(9)
where τn,r corresponds to the dust optical depth of template n with flux density Fn (λ), and it is required that
n > r for comparison. From this it is possible to deter-
9
mine the selective attenuation, Qn,r (λ),
Qn,r (λ) =
τn,r (λ)
,
l
δτBn,r
(10)
l
l
l
where δτBn,r
= τBn
− τBr
is the difference between the
Balmer optical depth of template n and r. We stress
that the quantity Qn,r (λ) reflects the selective attenuation, which is a difference in attenuation between two
wavelengths, and not a total attenuation, and because
of this the zero-point of Qn,r (λ) is arbitrary. Following
Calzetti et al. (1994), we select Qn,r (5500Å) = 0 as the
zero-point.
To determine the influence of variation in stellar population age for our galaxies we compared the entire sample
of galaxies spanning 0.8 . Dn 4000 . 1.6 to subsamples
spanning smaller ranges in Dn 4000. We find that using
the entire sample clearly affects the inferred attenuation
curve, Qn,r (λ), giving rise to artificially higher attenuation in the region of λ < 5500 Å as a result of the
slightly older stellar population ages for galaxies with
increasing τBl (i.e., the intrinsic spectrum of these systems is redder relative to reference bins). In light of
this, we adopt a window in average stellar population
age of 1.1 < Dn 4000 < 1.3 to derive our attenuation
curve. This subsample still encompasses the majority
of the sample (7265 galaxies), but works to restrict the
majority of the observed age effects.
The templates of the average flux density using these
galaxies divided into the same 6 bins of τBl shown in Table 1, but only using the 1.1 < Dn 4000 < 1.3 sample, can
be seen in Figure 7. It can be seen that the amplitudes
of the UV and optical flux density appear to be in good
agreement, which is more evident when we include the
average flux density in wavelength regions that contain
> 50% of the bin sample (dotted lines in Figure 7) and
the average u-band flux density. The x-axis error bar of
the average u-band flux density denotes the 1σ range in
rest-wavelength spanned in each bin. This suggests that
on average, our aperture corrections for the UV and optical flux density appear to provide values consistent with
each other. The similarity of template 1 and 2 is likely
a result of the distribution of galaxies in bin 1 having a
majority of cases towards τBl ∼ 0.1, which we show in
Figure 8 (also evident in the right panels of Figure 6),
and this is skewing the average SED of the template to
have similar attenuation to template 2.
We show the selective attenuation curve for each bin
of Balmer optical depth for different reference templates
in Figure 9. We exclude the use of template 1 in our
analysis because its SED appears so similar to template
2 (but with a lower average τBl ), a result which leads
to significantly lower selective attenuation curves when
it is used as a reference compared to those found using
the other templates. It can be seen in Figure 9 that
templates 2-6 all give very similar selective attenuation
curves. This implies that adopting a single selective attenuation curve is appropriate to characterize the entire
range of Balmer optical depths spanned by the majority
of galaxies in this sample. We determine the effective
attenuation curve, Qeff (λ), by taking taking the average
value of Qn,r (λ) found from templates 2-6. We have fit
the value of Qeff (λ) to a single third-order polynomial as
10
Battisti et al.
l , as a function of the 4000 Å break, (D 4000; top) and
Figure 6. The UV power-law index, βGLX , and the Balmer optical depth, τB
n
also the sSFR (sSFR = SFR/M∗ yr−1 ; bottom). A representative error bar of the median measurement uncertainties is shown in the top
l occur in galaxies with larger D 4000, which roughly
left of each panel. Slight trends appear to suggest that larger values of βGLX or τB
n
corresponds to older ages for the stellar population. A window of 1.1 < Dn 4000 < 1.3 (dashed red lines) is used to achieve a more uniform
l when deriving the average attenuation curve (see § 4.3). No clear trends are apparent with respect to
mean stellar age as a function of τB
sSFR.
a function of x = 1/λ (µm−1 ):
Qfit (x) = −2.488 + 1.803x − 0.261x2 + 0.0145x3 ,
0.125µm ≤ λ < 0.832µm . (11)
We compare our selective attenuation curve to other
curves in the literature in Figure 10. To give a sense
for the uncertainty, a gray region denoting the range of
Qn,r (λ) is shown (i.e., region spanned by all lines shown
in Figure 9). We include the curves of local starburst
galaxies from Calzetti et al. (2000), local SDSS galaxies from Wild et al. (2011), and higher redshift (z ∼ 2)
SFGs from Reddy et al. (2015). The selective attenuation
curves of Wild et al. (2011) are divided according to stellar mass surface density, µ∗ , with the break corresponding to the value which separates the bimodal local galaxy
population into bulge-less (µ∗ < 3 × 108 M⊙ kpc−2 ) and
bulged (µ∗ > 3 × 108 M⊙ kpc−2 ) galaxies (Kauffmann
et al. 2003b), as well as sub-divided by the sSFR and
the axial ratio (b/a). For clarity, we only reproduce the
−1
curves corresponding to log[sSFR (yr )] = −9.5 and
b/a = 0.6 from that work. The selective attenuation
curves of Reddy et al. (2015) are divided according to
sSFR. Our selective attenuation curve appears to be most
similar to the Calzetti et al. (2000) curve. We find that
the derived selective attenuation curve does not change
much depending on the range of Dn 4000 used, so long as
it remains relatively narrow (∆Dn 4000 . 0.2; see § 6.3).
The selective attenuation can be related to the totalto-select extinction, k(λ), through the following relation
k(λ) = f Q(λ) + RV ,
(12)
where f acts to change the tilt of the curve and is necessary to make k(B) − k(V ) ≡ 1,
f=
1
,
Qeff (B) − Qeff (V )
(13)
and where RV is the total-to-select extinction, which is
the vertical offset from 5500 Å. We assume B and V
bands to be 4400 Å and 5500 Å, respectively. The term
f is necessary to account for differences in the reddening between the ionized gas, which is assumed to suffer from extiction, and the stellar continuum. Therefore, the quantity f Q(λ) represents the true wavelengthdependent behavior of the attenuation curve on the stellar continuum, but does not represent a total attenuation
Characterizing Dust Attenuation in Local Star Forming Galaxies
11
l values for the sample of galaxies with
Figure 8. Histogram of τB
1.1 < Dn 4000 < 1.3. Vertical dotted lines denote the boundaries
for the bins adopted to construct the flux templates. The distril ∼ 0.25, resulting in the bins not
bution of sources is peaked at τB
being uniformly populated. This has a significant impact on the
average template constructed for bin 1, which appears similar to
template 2 as a result of the majority of sources in bin 1 lying at
l ∼ 0.1. For this reason, we do not use bin 1 in deriving the
τB
selective attenuation curve.
Figure 7. Average flux density of galaxies, normalized at 5500Å,
l for the subsample of galaxies with 1.1 <
within each bin of τB
l and the numDn 4000 < 1.3 (Ntot = 7265). The range in τB
ber of sources in each bin, Nbin , are shown in each panel. The
GALEX FUV and NUV flux densities for each galaxy are used to
determine the flux density over the region of 1250 < λ < 2600 Å
by assuming it follows βGLX . The optical measurements are from
SDSS spectroscopy. The gray regions denote the area enclosing
approximately 68% of the population. The dotted regions in the
optical spectra indicate the average obtained from less than the full
sample in that bin (due to varying redshifts), but still containing
> 50% of the bin sample. The symbols show the average u-band
flux density. It can be seen that the UV and optical flux densities seem to agree within the scatter, indicating that the aperture
corrections made are reasonable. For reference, the bottom panel
shows a comparison of the average flux density of each bin without
the dispersion included.
curve without knowledge of the normalization (given by
RV ). Determination of RV requires knowledge of either
the NIR photometry (where the attenuation should approach zero; k(λ → ∞) = 0) or the total infrared data
(to determine the total dust attenuation).
The value of f can be quantitatively expressed in terms
of the differential reddening between the ionized gas and
the stellar continuum by rewriting each term on the right
side of equation (10). For the case where the reference
source has τBl = 0, we get for the numerator
Fn (λ)
τn (λ) = − ln
= 0.921Aλ = 0.921E(B−V )star k(λ) ,
F0 (λ)
(14)
l
Figure 9. Selective attenuation curve, Qn,r (λ), for each bin of τB
(denoted by n) determined from comparing to a reference template
l . Also shown is the effective curve,
(denoted by r) at lower τB
Qeff (λ) (solid black line), which is the average value of Qn,r (λ)
for all cases, but excludes use of template 1 due to it appearing
nearly identical to template 2 (see § 4.3). The gap region between
2600 Å and 3800 Å is denoted with a dotted line corresponding to
a linear interpolation between the end points and is not used for
constraining the fit. The solid red line is a single polynomial fit to
Qeff (λ). The lower panel shows the difference between each curve
relative to Qeff (λ).
where we have used the definition of total-to-selective
extinction k(λ) ≡ Aλ /E(B − V )star , and for the denominator
l
δτBl = τBl − τB0
=
k(Hβ) − k(Hα)
E(B − V )gas , (15)
1.086
where k(Hβ) and k(Hα) are the values for the intrinsic
extinction curve of the galaxy and not from the attenu-
12
Battisti et al.
Figure 10. Comparison of our selective attenuation curve (red
solid line) compared to others in the literature. The gray region
denotes the range of Qn,r (λ) values (i.e., region spanned by lines in
Figure 9). The solid blue line is the starburst selective attenuation
curve of Calzetti et al. (2000), the dashed lines are the curves of
local SDSS galaxies from Wild et al. (2011) divided according to
stellar mass surface density, µ∗ , and the dash-dot lines are the
curves of z ∼ 2 SFGs from Reddy et al. (2015) divided according
to sSFR. Our selective attenuation curve appears most similar to
that found by Calzetti et al. (2000).
Figure 11. Normalized selective attenuation curve f Q(λ) derived
from our sample of SFGs compared to values in the literature
(f Q(λ) = k(λ) − RV ). The term f is required to make the curve
have k(B) − k(V ) ≡ 1. Lines are the same as in Figure 10 but with
the addition of the MW curve in solid black (Fitzpatrick 1999).
The gray region denoting the range of f Qn,r (λ) values (where f
varies in each case) is significantly reduced after this normalization.
We find a slightly lower selective attenuation in the UV compared
to previously determined attenuation curves, with a near-IR appearing similar to Calzetti et al. (2000).
ation curve. Therefore, we can rewrite the equation as
we find that the attenuation in SFGs is slightly lower in
the UV by up to 20% at 1250Å. Out towards the nearIR, our curve appears similar to the starburst curve from
Calzetti et al. (2000). If this similarity were to hold out
to longer wavelengths then we could expect the normalization term RV to be similar to the starburst curve value
of 4.05, since k(λ → ∞) = 0. An exact determination
of the value of RV for this curve will be the subject of a
future study.
If we assume the underlying extinction curve for these
galaxies to be the Fitzpatrick (1999) MW extinction
curve (for the values of k(Hβ) and k(Hα)), then we
find that hE(B − V )star i = 0.52hE(B − V )gas i for the
average of the SFGs in our sample. It is worth noting that assuming different extinction curves for the
ionized gas will result in subtle changes to this ratio
(e.g., for a Cardelli et al. (1989) MW extinction curve,
hE(B − V )star i = 0.45hE(B − V )gas i) and that the value
of k(λ) is likely to be dependent on metallicity. This is
important to consider when comparing values in the literature. This ratio is in agreement with previous results
suggesting that the stellar continuum suffers roughly onehalf of the reddening of the ionized gas (Calzetti et al.
2000; Kreckel et al. 2013).
Q(λ) =
E(B − V )star
k(λ) − RV
,
k(Hβ) − k(Hα) E(B − V )gas
(16)
where we have explicity added the term RV which corresponds to the zero-point normalization that was applied
at 5500 Å. Comparing this to equation (12) implies that
the term f is equivalent to
f=
k(Hβ) − k(Hα)
.
E(B − V )star /E(B − V )gas
(17)
For extinction curves, such as the Milky Way, it is the
case that E(B − V )star = E(B − V )gas , and f is simply
the difference in extinction between the Balmer emission lines. However, the same is not true of attenuation
curves for which it is typically seen that E(B − V )star <
E(B−V )gas (e.g., Calzetti et al. 2000; Kreckel et al. 2013;
Reddy et al. 2015).
The value of f for our average selective attenuation
curve, Qfit (λ), is determined using equation (11) to be
2.396+0.33
−0.29, where the uncertainty here reflects the maximum and minimum values from fits using individual
Qn,r (λ). We compare our selective attenuation curve
with this normalization term included to the attenuation curves mentioned before with their own f values, in
addition to the MW extinction curve in Figure 11. It
can be seen that the gray region denoting the range of
f Qn,r (λ) values, where f varies for each individual case,
is significantly reduced after this normalization. For reference, the values of f in other works are f = 2.659 in
Calzetti et al. (2000), f = 3.609 and 2.996 for the lower
and higher µ∗ sample, respectively, in Wild et al. (2011),
and f = 2.676 and 3.178 for the lower and higher sSFR
subsample, respectively, in Reddy et al. (2015). In reference to the attenuation curve from Calzetti et al. (2000),
5. SOURCES OF CONCERN IN ADOPTING βGLX FOR THE
UV SLOPE
5.1. Comparing βGLX to β
In order to compare the βGLX -τBl relationship found in
§ 4.1 to similar studies in the literature it will be necessary to understand how βGLX relates to the true UV
slope β estimated only from the UV continuum. The
GALEX filters have relatively wide passbands, which
makes them susceptible to numerous stellar absorption
features that appear in the UV. The influence of these
features is redshift-dependent because various absorption
Characterizing Dust Attenuation in Local Star Forming Galaxies
features will pass in and out of each filter as each passband shifts. In this section we seek to address whether
the differences in redshift for the galaxies in our sample is
affecting the observed βGLX -τBl relationship seen in § 4.1.
This will also allow us to transform βGLX to β and then
make comparisons to previous studies.
Typically the conversion factor between βGLX to β is
found using sample of galaxies for which both UV spectra and GALEX observations have been obtained (e.g.,
Kong et al. 2004; Takeuchi et al. 2012). These results
suggest that βGLX is typically larger (i.e., redder) than
β by ∼ 0.05 − 0.1. However, because UV spectral data
is not available for this sample, we utilize a Starburst99
(Leitherer et al. 1999) spectrum of a continuously star
forming galaxy with solar metallicity (Z⊙ = 0.02) as a
reference for an intrinsic galaxy spectrum. As will be
shown, the exact age of the reference spectrum is not
particularly important so long as the assumption of a
continuous SFR is reasonable, as the shape of the UV
slope remains relatively unaffected over a wide range of
ages (e.g., see Figure 2 of Leitherer et al. 1999). Working
from this reference spectrum we can apply an attenuation curve to vary the shape of the UV slope and then
shift the spectra to various redshifts. We will utilize the
attenuation curve that we derived in § 4.3. The lack
of the curve normalization is not important because we
are only examining the difference between βGLX and β,
and not the absolute values of the UV flux density (i.e.,
the shape of the UV SED after attenuation will remain
the same regardless of this normalization). Using a color
excess over the range 0.0 < E(B − V )star < 0.9 reproduces the full range of βGLX values seen in our sample.
For each reddened and redshifted spectrum we can then
determine what the corresponding value of βGLX is relative to β. The value of β is determined using the 10
rest-frame wavelength windows used by Calzetti et al.
(1994) to measure the UV slope of starburst galaxies
from the spectra observed by the International Ultraviolet Explorer (IUE) (βIUE ). These UV windows were
designed to avoid strong stellar absorption features, including the 2175 Å feature, and therefore represent an
accurate measure of the UV slope. As the windows are
taken in rest-frame wavelength, this measurement is not
affected by redshift.
The relationship between the two UV slope diagnostics
for several different redshifts is shown in Figure 12. For
each redshift, the steps in coverage correspond to changes
E(B − V )star of 0.036 starting at 0.0 in the lower-left and
increasing up to 0.9 in the upper-right. It can be seen
that for each redshift the relationship follows a simple
linear relation, βIUE = mβGLX + b, but with varying values of slope and offset. As expected, the value of βGLX
becomes more discrepant with βIUE as we move to higher
redshifts where more absorption features below 1250 Å
begin to come into the FUV filter passband. It is for
this reason that we imposed a redshift cut in our initial
sample selection of z < 0.1, in order to limit significant
deviations. It can be seen in Figure 12 that the differences between the two estimators for z < 0.1 is less
drastic than compared to higher z.
To determine the corrections, we take a linear leastsquares fit to the relation between βGLX and βIUE for
various redshifts. The behavior of the slope, m, and off-
13
Figure 12. The relationship between UV slope determined using
βGLX and βIUE for several different redshifts when adopting a SB99
model of a 100 Myr galaxy with continuous star formation. Each
symbol is a step in E(B − V )star of 0.036 starting at 0 in the
lower-left and increasing up to 0.9 in the upper-right, where we are
assuming the attenuation curve derived in § 4.3. For each redshift
the behavior follows a simple linear relation, demonstrated by the
linear least-squares fits (black lines). The dotted line shows the 1:1
relation.
set, b, as a function of redshift is shown in Figure 13.
We show the value of these parameters for several models with different ages of continuous star formation. As
expected, the variation among the parameters of the fit
are relatively small between the different models. The
100 Myr case seems to be a fair representation of the
average trend and so we will adopt it for determining
corrections.
The value of m behaves in a manner that can be well
approximated by a second-order polynomial. Fitting the
100 Myr case to this functional form gives
m(z) = 1.050 − 0.395z − 2.505z 2 .
(18)
The value of b behaves in a slightly more complicated
manner and is better fit using a fourth-order polynomial.
Fitting the 100 Myr case to this functional form gives
b(z) = −0.062 − 1.328z + 10.10z 2 − 152.4z 3 + 333.9z 4 .
(19)
By adopting these fits to the relationship between βGLX
and βIUE , we can reproduce the observed trends in Figure 12 very well. These conversion parameters are similar
to those found in other studies using more robust techniques (e.g., Kong et al. 2004; Takeuchi et al. 2012).
We examined if the assumption of the attenuation
curve is important in the conversion from βGLX to β
by by also using the (Calzetti et al. 2000) attenuation
curve. We find that differences in the conversion are not
significant over 0 < z < 0.1 (|∆m| . 0.02, |∆b| . 0.05),
and for this reason we do not expect this choice to have
a significant impact on the results.
The relationship between the UV slope, β, as a function of τBl is shown in Figure 14, where we have used the
average relation between βGLX and βIUE . The Spearman and Kendall nonparametric correlation tests give
ρS = 0.47 and τK = 0.32, respectively, for this relation.
Taking a linear least-squares fit gives
β = (1.95 ± 0.03)τBl − (1.61 ± 0.01) ,
(20)
14
Battisti et al.
Figure 13. The relationship between the slope, m, and the offset, b, in the fit of βIUE = mβGLX + b as a function of redshift for SB99
models with different ages of continuous star formation. There is relatively little variation in the behavior for the different age models (open
symbols). Our sample was restricted to z < 0.1, to limit the influence of absorption lines on the value of βGLX . We adopt the 100 Myr
case (green triangles) for our conversion, as it is a fair representation of the average trend. The behavior of the slope and offset are well
approximated by a second-order and fourth-order polynomials (red lines), respectively. The parameters of the fits to the 100 Myr values
are shown.
Figure 14. The UV power-law index after correcting for stellar
absorption features in the GALEX passbands, β (see § 5.1 for
conversion from βGLX ), as a function of the Balmer optical depth,
l , for our sample of SFGs. Symbols and lines have the same
τB
meaning as in Figure 3, however the values have changed.
with an intrinsic dispersion of σint = 0.44. Adopting
the same six ranges in τBl for the bins as before gives
a similar trend, with the values also given in Table 1.
The behavior of the relationship is similar to before with
nearly the same slope but with a lower offset by -0.15.
Now that the data has been expressed in terms of β,
our results can be directly compared to previous studies.
We compare our β − τBl relationship to the sample of
local starburst (SB) galaxies from Calzetti et al. (1994)
and also the sample of z ∼ 2 SFGs from Reddy et al.
(2015) in Figure 15. The relationship from Calzetti et
al. (1994) is βIUE = (1.76 ± 0.25)τBl − (1.71 ± 0.12),
and has a dispersion of σint ∼ 0.4. For the sample
of z ∼ 2 SFGs in Reddy et al. (2015), the authors
found significant variation in the β − τBl relationship
with sSFR (sSFR = SFR/M∗ yr−1 ). As a result of this
they separate their sample into two bins, βSED = (0.95 ±
0.14)τBl − (1.48 ± 0.02) for −9.60 ≤ log[sSFR] < −8.84
(σint = 0.31), and βSED = (0.87 ± 0.09)τBl − (1.78 ± 0.03)
for −8.84 ≤ log[sSFR] < −8.00 (σint = 0.20), where the
SED subscript denotes that this measurement is based
on using the 10 UV windows of Calzetti et al. (1994)
on best-fit stellar population models of the photometric
data.
Given the similarities with our attenuation curve with
Calzetti et al. (1994), it is not so surprising that Figure 15 shows that the β − τBl relationship of our sample
of SFGs is similar to their starburst sample. The overall
vertical offset could be linked to the intrinsic spectrum
of the starburst galaxies being a little bluer. In contrast,
we see a significantly different relation from the z ∼ 2
SFGs of Reddy et al. (2015). Such differences likely reflect variations in the geometry of the dust relative to the
ionized regions with redshift, but it could also result from
changes in the properties of dust grains (e.g., chemical
composition, absorption/scattering cross-sections, size
distribution) in galaxies with redshift. Although, the
range in sSFR values spanned by the sample in Reddy
et al. (2015, −9.6 < log(sSFR) < −8.0) is different from
that of our sample (−10.5 . log(sSFR) . −8.9). We explore the role that sSFR has in our local β − τBl relation
in more detail in § 6.2.
An interesting feature of the β − τBl relation is that
galaxies at the lowest dust attenuation (τBl ∼ 0) have
UV slopes which are still reddened (β ∼ −1.6) relative
to what is expected for a nearly dust-free system undergoing moderate star formation (β ∼ −2.2). This can
arise if the dust attenuation in star forming regions acts
in a different manner than the surrounding interstellar
medium (e.g., Charlot & Fall 2000; Calzetti 2001). Given
the observations, we expect a scenario in which the most
Characterizing Dust Attenuation in Local Star Forming Galaxies
Figure 15. Comparison of the UV power-law index, β, as a funcl , for our sample of SFGs (ortion of the Balmer optical depth, τB
ange line) to those in the literature. For each study β is determined
in a slightly different way, but in all cases it represents the UV slope
inferred from the stellar continuum (i.e., avoiding regions with stellar absorption features, see § 5.1 for details). We show the Calzetti
et al. (1994) sample of starburst galaxies (black line) and the SFGs
at z ∼ 2 from Reddy et al. (2015), which are separated according
to sSFR (sSFR = SFR/M∗ yr−1 ; red and blue lines). Our fit at
l > 0.7 is shown with a dashed line to denote that there are
τB
limited data in this range. The intrinsic dispersion of our data is
denoted by the gray filled region (σint = 0.44). The dispersion of
the other samples are not shown for clarity.
active star forming regions of the galaxy can be dust obscured but not “seen” in the Balmer decrement. This is
possible if some dust is homogeneously mixed with stars
in the star forming regions, as such a geometry will result
in overall attenuation which is gray (e.g., Calzetti 2013).
More specifically, the flux density of the star forming regions will be significantly reduced relative to the older
population, such that it does not contribute to the observed UV slope, but which still provides an observed
Balmer decrement which is similar to the intrinsic value.
Such a scenario has been seen in star clusters (Calzetti et
al. 2015), and can explain the appearance of UV reddening despite the optical diagnostics that suggest minimal
attenuation from the interstellar medium.
5.2. Disentangling the Influence of a 2175Å Feature
A characteristic feature of the MW extinction curve is
the dust feature at 2175 Å (see Figure 11). It is well
known that the presence of scattering for an extended
source by a foreground dust screen has the effect of reducing the overall optical depth, flattening the attenuation curve, and diminishing the strength of the 2175 Å
feature (Natta & Panagia 1984; Calzetti et al. 1994). In
addition, it has been suggested that the strength of the
UV field may affect the dust that produces this feature
(e.g., Gordon et al. 2003). Together, these effects can
explain the absence of this feature from the starburst
attenuation curve (Calzetti 2001). However, a 2175 Å
feature has been seen to some extent in the attenuation
curve of other local (e.g., Conroy et al. 2010; Wild et al.
2011) and high-redshift galaxies (e.g., Noll et al. 2009;
Buat et al. 2011, 2012; Kriek & Conroy 2013; Scoville
et al. 2015). In this section we will address the effects
that such a feature would have on our observations if it
persisted to some degree.
15
Figure 16. The Milky Way extinction curve and the corresponding value inferred from a convolution of GALEX bands over the
redshift range of our sample (0 < z < 0.1). The wide passband of
the NUV acts to suppress the strength of a 2175 Å feature, thus
making it more difficult to detect the presence of a feature.
In Figure 16, we show the location of the FUV and
NUV bands as a function of redshift relative to the MW
extinction curve. It can be seen that for the redshift
range of our sample (0 < z < 0.1), the 2175 Å feature
always lies within the GALEX NUV filter. The limited
nature of our UV coverage also implies that we cannot
separate our sample into redshift bins to determine underlying differences in the shape of the UV continuum.
Therefore, there is a legitimate concern whether such a
feature can be influencing the derived values of the UV
slope in this work. Despite our inability to directly measure the presence of the 2175 Å feature, we provide several considerations below which suggest that on average
it is quite weak in our sample.
First, the presence of a 2175 Å feature can only make
a UV spectrum, as measured by βGLX , appear bluer.
We demonstrate this effect by showing the results of
adding a MW-like 2175 Å feature of varying strength
to the Calzetti et al. (2000) starburst attenuation curve
on a template with a fixed UV slope. The strength of
the 2175 Å feature is crudely determined by subtracting off the excess extinction in the MW curve between
1600−2850 Å assuming an underling linear relation. The
nature of this method, along with the modified SB attenuation curves, are shown in Figure 17. For the purpose
of comparing effects on βGLX , we offset the β-τBl relation from Calzetti et al. (1994) by the average difference found in our sample due to stellar absorption lines
(βGLX ∼ β + 0.15; see § 5.1). For simplicity, the template assumed is a smooth UV flux density profile with
β = −1.56 (F = λβ ), which is chosen because it is similar
to the zero-point of the offset of the Calzetti et al. (1994)
relation. To determine βGLX as a function of τBl for each
attenuation curve, we vary E(B − V )gas , which relates
to τBl through equation 4, and assume hE(B − V )star i =
0.44hE(B − V )gas i (Calzetti et al. 2000) to attenuate the
template (Fobs = Fint 10−0.4E(B−V )star k(λ) ). Looking at
Figure 18, it is apparent that the βGLX -τBl relation is flatter as the strength of a 2175 Å feature is increased. This
16
Battisti et al.
Figure 17. As a test of the presence of a Milky Way-like 2175 Å
feature in our attenuation we can determine if adding a similar
feature to the Calzetti et al. (2000) attenuation can reproduce the
differences between that attenuation curve and the one we are finding. To achieve this we assume a linear relation underlying the
2175 Å feature and subtract off the bump feature. The residual
bump, kbump , can then be added to the Calzetti et al. (2000) at
various strengths.
trend occurs because the added absorption within the
NUV passband from the feature results in the observed
UV slope appearing bluer. Since we do not observe a
flatter relation in comparison to that of Calzetti et al.
(1994), this would argue against a significant feature in
the attenuation curve. In addition, if the strength of
the feature were to vary significantly over the sample we
would expect to see a larger dispersion in the observed
βGLX -τBl relation at larger τBl , which does not appear to
occur in Figure 3. However, given the large scatter of
the observed βGLX -τBl relation, a more subtle influence
of such a feature cannot be ruled out.
Second, if an absorption feature is affecting the NUV
flux density, then we would expect to see discrepancies
in the appearance of the UV-optical spectra seen in Figure 7. Any absorption in the NUV band would lead to
a bluer looking slope, which in turn would cause large
offsets between the estimated flux density at 2600 Å and
the start of the SDSS spectra at ∼4000 Å. Following the
previous argument, the presence of a feature would additionally manifest itself in the derived selective attenuation curve (Figure 9), resulting in an offset between
the UV and optical regions. Such a feature would cause
larger values of Q(λ) for the NUV portion, which does
not appear to be the case because they are all well approximated by a single third-order polynomial over the
entire UV-optical wavelength region.
Since we do not see the influence of a 2175 Å feature
in our average attenuation curve, we can rule out that it
is playing a significant role in the average SFG. However,
more detailed analysis of the UV spectrum, ideally with
spectroscopy, should be pursued to determine this conclusively. Such analysis is beyond the immediate scope
of this work.
6. DISCUSSION
6.1. Influence of Galaxy Properties on Dust Attenuation
l relation found using the Calzetti et al.
Figure 18. The βGLX -τB
(2000) attenuation curve, k(SB), modified with an added 2175 Å
feature at various strength relative to the MW (dashed lines).
These curves are applied to a smooth UV flux density profile with
β = −1.56 (chosen because it has an intrinsic UV slope similar
to the zero-point of the observed relations). It can be seen that
adding this feature acts to keep the observed UV slope bluer as a
l , a result of the extra attenuation in the NUV band.
function of τB
Since such a trend is not seen in our sample relative to the Calzetti
et al. (1994) relation, this would suggest that such a feature is not
significant in a majority of these galaxies.
Since the dust in these galaxies is giving rise to the
observed attenuation, one would naturally expect correlations to exist between parameters that are strong
indicators of the presence of dust. The two ingredients needed for significant dust content in a galaxy are
high metal content and high gas content (e.g., Calzetti
& Heckman 1999). Previous studies have found a positive correlation between the total dust mass in galaxies with their gas-phase metallicity (Draine et al. 2007;
Galametz et al. 2011), however the functional form of this
relation is still under considerable debate. In addition,
there are the well-known positive correlations between
stellar mass and metallicity (e.g., Tremonti et al. 2004)
and stellar mass and SFR, also called the star forming
main-sequence (e.g., Brinchmann et al. 2004; Cook et al.
2014). Taken together, these relations suggest a scenario
in which the most massive galaxies and/or actively star
forming galaxies accumulate a larger amount of dust that
can lead to elevated levels of attenuation compared to
their low mass and/or weakly star forming counterparts.
A relation between SFR and amount of dust attenuation
is observed, for instance, in local galaxies (e.g., Wang
& Heckman 1996; Calzetti 2001). However, the requirement of high gas content implies that there will eventually be a turnover in this behavior as one moves to the
most massive galaxies, which are dominated by elliptical
galaxies. This is a consequence of the baryon efficiency of
galaxies experiencing a turnover at around M∗ , implying
a gas-deficiency in the most massive galaxies (e.g., Guo et
al. 2010). Such a scenario naturally explains why massive
elliptical galaxies typically have negligible dust content.
Unfortunately, the complex nature of the many physical mechanisms giving rise to the correlations mentioned
above have made quantifying this picture difficult.
Here we explore the presence of correlations between
Characterizing Dust Attenuation in Local Star Forming Galaxies
observational parameters associated with dust attenuation and various galaxy properties in order to help understand which properties are important for the presence
of dust. In this section we will make use of β for the
UV slope in order to limit systematic effects with redshift. We examine the relationships between β and τBl
with the metallicity, stellar mass, SFR, and SFR surface
density (ΣSFR ) of the galaxies. We plan to examine the
role of galaxy inclination on attenuation in a future paper. As a reminder, we utilize the measurements of these
quantities within the 3′′ SDSS fiber, along with their 1σ
uncertainties, derived by the MPA/JHU group. The resulting comparisons are shown in Figure 19. Looking at
this Figure, it is evident that tighter relationships arise
for τBl than for β. Part of this is likely due to the smaller
uncertainties in former quantity, but it is also the case
that differences in the underlying SFH of these galaxies could have a larger influence on the UV luminosity,
and hence the UV slope. As has been found in many
previous studies, the trends here suggest that star forming galaxies with larger metallicities, stellar masses, and
star formation rates tend to have higher dust attenuation (e.g., Wang & Heckman 1996; Hopkins et al. 2001;
Garn & Best 2010; Reddy et al. 2015). We perform a
simple second-order polynomial fit to the data shown in
Figure 19, to illustrate the general trends. We stress that
these fits do not formally account for the uncertainties in
the parameters and should only be used as a guideline.
We present each fit, along with the intrisic dispersion
from this relation, in Table 2. In this table, we also show
the coefficients for the Spearman, ρS , and Kendall, τK ,
nonparametric correlation tests, which act as a gauge of
the correlation strength. Similar to before, the large sample size makes the probability of no correlation be very
close to zero and no longer meaningful to report.
For comparison, we plot the relationships found in
Garn & Best (2010) using the full SDSS SFG dataset
(∼100000 galaxies) for Hα attenuation, AHα as a function of metallicity, stellar mass, and SFR in Figure 19.
We convert AHα back into a Balmer decrement following their assumption of a Calzetti et al. (2000) attenuation curve (see their equation (1)), and then convert that
into τBl using equation (3). For consistency, we convert
their metallicity values, derived using the O3N2 indicator
(Pettini & Pagel 2004), into Tremonti et al. (2004) values
using the relation provided in Kewley & Ellison (2008).
As expected, we find that the relationship we see with
metallicity is nearly identical to theirs, although we do
not see any evidence of a turnover at high metallicities as
they suggest. However, significant differences appear between our relationships and those of Garn & Best (2010)
for τBl as a function of stellar mass and SFR. This is a result of their use of total galaxy values for stellar mass and
SFR, whereas we utilize fiber measurements, because the
Balmer decrement measurement in both studies are coming from only the fiber region (same τBl values) but the
enclosed stellar mass and SFR are aperture dependent.
The aperture-dependence of these values gives rise to the
horizontal offset between the relations. In their analysis
Garn & Best (2010) assume that the Balmer decrement
is not dependent on the fiber aperture, which has been
found to hold in some studies albeit with a large dispersion among individual cases (e.g., Kewley et al. 2005;
17
Zahid et al. 2013). However, other studies have found radial dependencies which suggest the Balmer decrement
decreases with increasing radius (e.g., Muñoz-Mateos et
al. 2009; Iglesias-Páramo et al. 2013), with more massive galaxies having larger gradients (Nelson et al. 2015).
Given the inconclusive nature of this effect, we choose
not to make assumptions regarding the aperture corrections for the attenuation, as we want all comparisons to
be as self-consistent as possible.
Understanding the general relationships between the
amount of attenuation and these parameters offers a potential avenue for determining appropriate dust corrections at higher redshifts. However, several studies have
found that the relationship between dust attenuation and
SFR appears to evolve with redshift (e.g., Reddy et al.
2006, 2010; Sobral et al. 2012; Domı́nguez et al. 2013).
The studies of Sobral et al. (2012) and Domı́nguez et al.
(2013) also examined the relation between dust attenuation and total stellar mass and find that it does not show
significant evolution from redshift z = 0.1 to 1.5 when
comparing to Garn & Best (2010). As a consequence,
they state that total stellar mass might be a fundamental predictor of dust attenuation corrections. However,
since we find an offset relative to the Garn & Best (2010)
relation when using fiber-only measurements (due to less
mass being enclosed), this result suggests that the relation between dust attenuation and total stellar mass
is not fundamental. We suspect that the correlations
between the attenuation and stellar mass or SFR is a
byproduct of their strong correlation with metallicity
and/or gas content, which are more fundamental predictors for the presence of dust. Additional studies are
needed to determine if the relationship between attenuation and metallicity is redshift-dependent.
l
6.2. Variation in β-τB
Given the large number of sources in our sample, we
can also examine the variation in the behavior of the
β-τBl relation for galaxies with specific properties and
identify key drivers of the large intrinsic scatter. Recent findings by Reddy et al. (2015) examining SFGs at
z ∼ 2, found that galaxies appear to show significant
differences in the β-τBl relation as a function of galaxy
sSFR. We separate our sample into three subsamples according to Dn 4000 and sSFR, as these may be expected
to correlate to the intrinsic UV slope. We also divide
the sample by z in order to test whether a fixed aperture with redshift influences the measurements. The results are shown in Figure 20. We chose the subsamples
to consist of roughly one-third of the sample (∼ 3000
galaxies). We note regions with low sampling of galaxies with dashed lines. Looking at Figure 20, it can be
seen that no significant differences are evident in the β
vs τBl relation with Dn 4000, sSFR, or z, which indicates
that the intrinsic scatter is not driven primarily by these
parameters. We do not observe large variations in the
offset of β with sSFR, as is seen in Reddy et al. (2015),
but we note these studies probe different regimes, with
the bin of highest sSFR (−9.6 < log[sSFR] < −8.9) in
our sample corresponding to the bin of lowest sSFR their
sample (−9.6 < log[sSFR] < −8.84), which makes direct
comparison difficult.
We find that it is not particularly informative to divide the sample according to galaxy metallicity, mass,
Battisti et al.
Table 2
l as a Function of Galaxy Properties
Fit Parameters of β and τB
l
τB
β
x
12+log(O/H)
log[M∗ (M⊙ )]
log[SFR (M⊙ yr−1 )]
log[ΣSFR (M⊙ yr−1 kpc−2 )]
range
8.1 < x < 9.2
7.4 < x < 10.4
−2.5 < x < 1.0
−2.6 < x < −0.2
p0
85.55
2.334
-9.115×10−1
-1.651×10−1
p1
-20.95
-1.140
4.131×10−1
9.349×10−1
p2
1.261
8.392×10−2
9.833×10−2
1.897×10−1
σint
0.45
0.46
0.47
0.46
ρS
0.44
0.43
0.36
0.37
τK
0.33
0.30
0.25
0.26
p0
29.55
2.561
3.585×10−1
5.940×10−1
p1
-7.177
-6.984×10−1
1.962×10−1
2.402×10−1
p2
4.370×10−1
4.889×10−2
3.078×10−2
9.625×10−3
σint
0.11
0.11
0.11
0.11
ρS
0.72
0.72
0.68
0.67
τK
0.52
0.53
0.50
0.49
18
Notes. The functional form of these fits are y = p0 + p1 x + p2 x2 . We also report the intrinsic dispersion, σint , which is taken as the standard deviation from the fitted relation. These
fits are performed without accounting for the uncertainties in the variables and are only intended to illustrate general trends. The coefficients for the Spearman, ρS , and Kendall, τK ,
nonparametric correlation tests are also given for each case.
Characterizing Dust Attenuation in Local Star Forming Galaxies
19
Figure 19. The UV power-law index after correcting for stellar absorption features in the GALEX passbands, β (see § 5.1),, and the Balmer
l , as a function of various galaxy properties. Shown from top to bottom are the gas-phase metallicity, stellar masses, SFRs,
optical depth, τB
and SFR surface density (ΣSFR ), respectively (all from 3′′ SDSS fiber). A representative error bar of the median measurement uncertainties
is shown in the top left of each panel. All quantities show a positive correlation with the amount of UV and optical attenuation. Secondorder polynomial fits to the data are shown as the solid red lines, with the dispersion shown as dotted red lines (±σint ). When possible,
we compare to Garn & Best (2010), which are offset in M∗ and SFR due to their use of total quantities in contrast to our fiber-only values
(see § 6.2).
20
Battisti et al.
SFR, or ΣSF R because these show significant correlation with the attenuation parameters, which implies that
these parameters segregate galaxies in β-τBl parameter
space. As a result, this makes it difficult to differentiate between variation in attenuation relations because
low and high attenuation galaxies would be separated.
As an example, we illustrate the sample separated into
three equally spaced bins in metallicity, which is argueably more informative here instead of equal number bins,
in Figure 20. It can be seen that the higher metallicity
galaxies (8.8 < 12 + log(O/H) < 9.2), which correspond
to the majority of our sample, are driving much of the
observed trend between β and τBl .
6.3. Variation in the Attenuation Curve
In a similar manner to how the sample was divided
to see the effect on the observed values of β and τBl ,
we can now examine how the attenuation curve changes
with these properties. We utilize the same subsamples
presented in § 6.2 of Dn 4000, sSFR, and z. For each parameter except Dn 4000, we add an additional constraint
that 1.1 < Dn 4000 < 1.3 in order to limit the stellar
population age effects. We follow the same methodology
presented in § 4.3, dividing each sample into 6 bins of τBl
and constructing average flux templates, to derive the
attenuation curve for these subsamples. We do not consider bins with less than 100 galaxies in determination
of the effective attenuation curve. For nearly all cases
the effective attenuation curve in the UV (derived from
βGLX ) and optical (derived from SDSS spectra) appear
to be in agreement and well approximated by a single
third-order polynomial. All of the fits to these subsamples are presented in Table 3.
We plot the subsample curves of Q(λ) alongside our
average curve derived earlier and the Calzetti et al.
(2000) curve (left panels), as well as the curves normalized by f and alongside the Fitzpatrick (1999) MW
curve (right panels), in Figure 21. Slight differences
in Q(λ) appear in the Dn 4000 and sSFR subsamples,
with the latter case being more significant. If we make
the crude assumption that these galaxies have similar
extinction curves, then this would indicate variation in
hE(B − V )star i/hE(B − V )gas i. These differences suggest
that galaxies with lower Dn 4000 or higher sSFR have
slightly higher ratios of hE(B − V )star i/hE(B − V )gas i
(lower f ). These changes are quite interesting because
they indicate differences in the relative reddening of the
ionized gas and the stellar continuum. One possible explanation for this is that in galaxies with elevated SFRs
the UV reddening is more heavily weighted towards the
same regions that dominate the Balmer line emission,
thus increasing hE(B − V )star i/hE(B − V )gas i. One can
imagine that for the extreme scenario in which nearly
all of the global flux density is exclusively produced in
HII regions, that this ratio would approach unity. However, this behavior is dependent on the optical depth of
these star forming regions. In their study of z ∼ 2 SFGs,
Reddy et al. (2015) find a lower ratio with increasing
sSFR which they attribute to a larger fraction of the star
formation in the galaxy becoming obscured in optically
thick regions as the SFR increases. These obscured regions do not contribute significantly to the UV emission,
but they continue to contribute to the Balmer line emission. Thus, the UV slope underestimates the dust atten-
uation relative to the Balmer line inferred attenuation for
these galaxies such that hE(B − V )star i/hE(B − V )gas i
decreases toward larger SFRs. It is important to note
that a lower ratio of hE(B − V )star i/hE(B − V )gas i is
also possible if higher star formation activity gives rise
to significant outflows which reduce the overall optical
depth affecting the stellar continuum. It is also important to state again that the sample of Reddy et al. (2015)
probes a higher range of sSFR than this work and this
may lead to differences in the underlying physical mechanisms at work between the two samples. Given the complex dependence of this ratio, we can not make any clear
statement as to the cause of the differences that we see
in our sample.
Another notable result that can be seen in Figure 21
is that there is virtually no dependence on the behavior of the attenuation curve as a function of the redshift
spanned by our sample. We take this to indicate that
the different physical aperture scales being probed as a
result of our choice of fixed angular aperture does not
seem to significantly alter the resulting curve. This also
indicates that the average attenuation properties over
smaller galaxy regions do not significantly deviate from
the total values.
Despite the changes seen in the behavior of Q(λ) with
proxies for stellar age, after normalizing the curves as
f Q(λ) the difference in the curves is significantly reduced
in all cases (see right panels of Figure 21). A similar result was found by Reddy et al. (2015) for their z ∼ 2
sample of galaxies separated by sSFR, albeit with a different overall shape than we find for local galaxies. This
remarkable result indicates that despite the differences in
physical properties and SFHs that are spanned by SFGs
in the local universe, on average they appear to suffer
from a similar attenuation curve. However, the large
scatter in the β-τBl relation and the flux density SEDs
likely implies that there are variations in the attenuation on a case-by-case basis, part of which can stem from
differences in the star-dust geometry.
7. CONCLUSIONS
We use a sample of ∼10000 local (z . 0.1) star forming galaxies to constrain the nature of dust attenuation in
galaxies as a function of their physical properties. Utilizing aperture-matched UV and optical data, we find
a linear relationship between the UV power-law index,
β, and the Balmer line optical depth, τBl , which is similar to the local starburst relation. The large scatter
(σint = 0.44) of this relation suggests there is significant
variation in the attenuation of individual galaxies local
Universe. Using this large sample, we are able to quantify how the attenuation is influenced by varying galaxy
parameters. We observe significant correlations between
the amount of UV and ionized gas reddening with galaxy
metallicity, M∗ , SFR, and ΣSFR . A weaker negative correlation is seen with the mean stellar age, traced by the
4000 Å break (Dn 4000). These trends are consistent with
a scenario in which the total dust content increases with
star formation activity and also builds up slowly with
age. These relationships can provide a way for determining attenuation in other studies if these parameters are
available. However, we stress that the redshift evolution
of some of these relationships (e.g., Reddy et al. 2006,
2010; Sobral et al. 2012; Domı́nguez et al. 2013) poses a
Characterizing Dust Attenuation in Local Star Forming Galaxies
21
l relation for subsamples of galaxies with different properties (β is the UV power-law index after correcting for stellar
Figure 20. The β-τB
absorption features, see § 5.1). The parameters considered here are Dn 4000, sSFR, z, and gas-phase metallicity. Only small differences
appear among the different subsamples, which are not significant given the scatter in the data. In addition, the intrinsic dispersion is not
l with metallicity isolates
seen to decrease among these subsamples. The lower panel acts to illustrate that the strong correlation of β and τB
different regions of parameter space.
problem in the application to higher redshift studies.
Using our sample we derive an attenuation curve over
the wavelength range 1250Å < λ < 8320Å. We find a
lower selective attenuation in the UV compared to previously determined attenuation curves and which is about
20% lower than the starburst curve from Calzetti et al.
(2000) at 1250Å. However, given that the normalization
of our curve is still unknown, it is not clear whether
this also corresponds to lower total attenuation. Such
an analysis will be the subject of a future study. We see
no evidence to suggest that a significant 2175 Å feature
is present in this curve, although this cannot be conclusively determined without available UV spectroscopy.
The relative reddening of the stellar continuum is roughly
one-half of the amount suffered by the ionized gas, with
hE(B − V )star i = 0.52hE(B − V )gas i (assuming Fitzpatrick (1999) MW extinction for the ionized gas), in
good agreement with previous studies (Calzetti et al.
1994; Wild et al. 2011; Kreckel et al. 2013; Reddy et
al. 2015). We emphasize that this is the average rela-
22
Battisti et al.
Table 3
Fit Parameters of Q(λ) as a Function of Galaxy Properties
x
Dn 4000
range
1.1 < x < 1.3
1.016 < x < 1.185
1.185 < x < 1.251
1.251 < x < 1.418
f
+0.33
2.396−0.29
+0.31
2.283−0.26
+1.18
2.840−0.35
+1.16
2.840−0.58
p0
-2.488
-2.565
-2.139
-2.138
p1
1.803
1.823
1.551
1.567
p2
-2.609×10−1
-2.510×10−1
-2.320×10−1
-2.358×10−1
p3
1.452×10−2
1.332×10−2
1.373×10−2
1.364×10−2
log[sSFR (yr−1 )]
−10.50 < x < −9.90∗
−9.90 < x < −9.60∗
−9.60 < x < −8.90∗
+0.22
2.580−0.26
+0.58
1.931−0.26
+0.45
1.804−0.27
-2.423
-3.065
-3.185
1.817
2.225
2.275
-2.862×10−1
-3.168×10−1
-3.063×10−1
1.636×10−2
1.664×10−2
1.567×10−2
z
0.002 < x < 0.045∗
0.045 < x < 0.069∗
0.069 < x ≤ 0.105∗
+0.36
2.302−0.38
+0.36
2.296−0.41
+0.32
2.260−0.16
-2.642
-2.488
-2.584
1.931
1.759
1.859
-2.913×10−1
-2.317×10−1
-2.572×10−1
1.717×10−2
1.169×10−2
1.321×10−2
Notes. The uncertainty in f denotes the maximum and minimum values from fits using individual Qn,r (λ) for each subsample (see § 4.3).
The functional form of these fits are Q = p0 + p1 x + p2 x2 + p3 x3 . ∗ These cases also have the constraint that 1.1 < Dn 4000 < 1.3.
tion and that individual cases will vary from this ratio
depending on their properties.
When dividing the sample according to different galaxy
properties we find that galaxies with larger sSFRs have
smaller f values (larger ratios of hE(B − V )star i/hE(B −
V )gas i). However, after normalizing the curves to remove
the effects of differential reddening, the variation in the
curves is significantly reduced in all cases. This result
indicates that despite differences in physical properties
and SFHs spanned by SFGs in the local universe, on
average they appear to suffer from a similar underlying
attenuation curve. This single attenuation curve is well
suited for application to large statistical studies of SFGs,
but should be used with caution on a case-by-case basis.
ACKNOWLEDMENTS
The authors thank the anonymous referee whose suggestions helped to clarify and improve the content of this
work. AJB also thanks K. Grasha for comments that improved the clarity of this paper.
Part of this work has been supported by NASA, via the
Jet Propulsion Laboratory Euclid Project Office, as part
of the “Science Investigations as Members of the Euclid
Consortium and Euclid Science Team” program.
This work is based on observations made with the
NASA Galaxy Evolution Explorer. GALEX is operated
for NASA by the California Institute of Technology under
NASA contract NAS5-98034. This work has made use of
SDSS data. Funding for the SDSS and SDSS-II has been
provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation,
the US Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society and the Higher Education Funding Council for England. The SDSS website
is http://www.sdss.org/. The SDSS is managed by the
Astrophysical Research Consortium for the Participating
Institutions.
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APPENDIX
VIABILITY OF USING THE OPTICAL SLOPE INSTEAD OF THE UV SLOPE
Future large area IR surveys, such as those planned with Euclid and the Wide-Field Infrared Survey Telescope
(WFIRST ), will image vast numbers of galaxies. Given the shortest wavelengths available to these missions, ∼ 5500 Å
and ∼ 7600 Å for Euclid and WFIRST, respectively, the shortest rest-frame wavelengths available for galaxies with
z < 1 this will correspond to the optical portion of the spectrum. Therefore, a proper utilization of the β-τBl relation
would require separate measurements from another facility to determine UV slope. Here we investigate the possibility
of using the optical slope, from the observed SDSS u (λeff = 3543 Å) and g (λeff = 4770 Å) fiber photometry, as an
indicator for reddening of the continuum instead of β. This is calculated using the same method as for the UV slope,
βopt =
log[Fλ (u)/Fλ (g)]
.
log(λu /λg )
(A1)
We expect that the correlation between the optical slope and τBl to be weaker than the UV slope, given that this
region is less sensitive to the effects of dust and more sensitive to older stellar populations.
In Figure 22 we show the βopt and τBl values for our sample of 9813 SFGs. A linear fit to the data using the
MPFITEXY routine (Williams et al. 2010) gives
βopt = (2.32 ± 0.04)τBl + (0.71 ± 0.01) ,
(A2)
with an intrinsic dispersion of σint = 0.53. As expected, this dispersion is larger than that found using the UV slope,
but not by a very large amount. Similar to earlier anaylsis, we divide the sample by Dn 4000 to determine its role in
the dispersion. We plot the sample divided into three ranges of Dn 4000 in Figure 23 and the fitted relationships are
βopt (1.018 < Dn 4000 < 1.185) = (1.04 ± 0.06)τBl + (0.67 ± 0.01) ,
(A3)
βopt (1.185 < Dn 4000 < 1.251) = (0.87 ± 0.04)τBl + (1.12 ± 0.01) ,
(A4)
βopt (1.251 < Dn 4000 < 1.418) = (1.43 ± 0.04)τBl + (1.29 ± 0.02) .
(A5)
It is evident that the dispersion is reduced by ∆σint ∼ −0.15. This indicates that Dn 4000 acts as an indicator of the
intrinsic optical slope (i.e., the normalization of the βopt − τBl relation). From this we believe that the optical slope
might be viable for determining appropriate corrections in a large statistical sample, especially if information on the
4000Å break is available to correct for stellar age effects.
Characterizing Dust Attenuation in Local Star Forming Galaxies
25
l , for our sample of SFGs (orange line). A
Figure 22. The optical power-law index, βopt , as a function of the Balmer optical depth, τB
l
representative error bar for the SFG sample is shown in the bottom right. Our fit at τB > 0.7 is shown with a dashed line to denote that
there are limited data in this range.
l relation for subsamples of galaxies with different D 4000. The subsamples show significant offsets relative to
Figure 23. The βopt -τB
n
each other and also have a lower dispersion relative to the total sample. This indicates that Dn 4000 acts as a good diagnostic of the
intrinsic optical slope (i.e., vertical normalization). Galaxies with an older stellar population (larger Dn 4000) have a redder intrinsic values
of βopt .